Author: damir

2019 Workshop: “If” by any other name

UConn Logic Group Workshop, April 6-7, 2019

“If” by any other name

It is a relatively recent development that research on conditionals is taking a deep and sustained interest in the full range of linguistic markers, their interactions with each other and with other linguistic categories, and the ways in which they drive and constrain the interpretation of the sentences they occur in. Tense and aspect is an area where such attention has already borne fruit; to a lesser extent, we may mention conditional connectives and pro-forms (especially thanks to works like Iatridou 2000 and Iatridou & Embick 1993). More recently, there seems to be a growing interest in two things: on the one hand, more varied aspects of formal marking of conditionals and the ways in which different grammatical categories may be recruited to encode conditional meaning (including aspect, different types of connectives, conjunctions, etc.); on the other hand, the appearance of these markers in other linguistic contexts (like optatives, complement clauses, temporal clauses, interrogatives, etc.).

Program

Saturday, April 6

12:00-2:00: Kai von Fintel & Sabine Iatridou (MIT) “Prolegomena to a Theory of X-Marking”

2:30-3:15: Muyi Yang (UConn) “Explaining negative counterfactuals”
3:15-4:00: Teruyuki Mizuno (UConn) “The structure of might-counterfactuals: a view from Japanese”

4:30-5:30: Paolo Santorio (UC San Diego) “The Double Life of Antecedent Strengthening”

Sunday, April 7

10:00-11:00: Una Stojnić (Columbia): t.b.a.

11:15-12:00: Hiromune Oda (UConn): t.b.a.

1:30-2:30: Will Starr (Cornell) “Indicative Conditionals, Strictly”
After 2:30: coffee & discussion as desired

Recursive counterexamples and the foundational standpoint

Benedict Eastaugh

Recursive counterexamples are classical mathematical theorems that are made false by restricting their quantifiers to computable objects. Historically, they have been important for analysing the mathematical limitations of foundational programs such as constructivism or predicativism. For example, the least upper bound principle is recursively false, and thus unprovable by constructivists. In this talk I will argue that while recursive counterexamples are valuable for analysing foundational positions from an external, set-theoretic point of view, the approach is limited in its applicability because the results themselves are not accessible to the foundational standpoints under consideration. This limitation can be overcome, to some extent, by internalising the recursive counterexamples within a theory acceptable to a proponent of a given foundation; this is, essentially, the method of reverse mathematics. I will examine to what extent the full import of reverse mathematical results can be appreciated from a given foundational standpoint, and propose an analysis based on an analogy with Brouwer’s weak and strong counterexamples. Finally, I will argue that, at least where the reverse mathematical analysis of foundations is concerned, the epistemic considerations above show that reverse mathematics should be carried out within a weak base theory such as RCA0, rather than by studying ω-models from a set-theoretic perspective.

De Re and De Dicto Knowledge of Mathematical Statements

Marianna Antonutti

In this talk, I will apply the de re/de dicto distinction to the analysis of mathematical statements and knowledge claims in mathematics. A proof will be said to provide de dicto knowledge of a mathematical statement if it provides knowledge of a purely existential statement, and to provide de re knowledge when it carries additional information concerning the identity criteria for the objects that are proven to exist. I will examine two case studies, one from abstract algebra and one from discrete mathematics, and I will suggest that reverse mathematics can help measuring the ‘de re content’ of two different proofs of the same theorem, and that the de re/de dicto distinction introduced here lines up with certain model theoretic properties of subsystems of second order arithmetic, such as the existence of certain kinds of minimal model. Furthermore, I will argue that there are good reasons not to identify the de re content of a proof with its constructive content nor with its predicative content.

How to model the probabilities of conditionals

Branden Fitelson

David Lewis (and others) have famously argued against Adams’s Thesis (that the probability of a conditional is the conditional probability of its consequent, given it antecedent) by proving various “triviality results.” In this paper, I argue for two theses — one negative and one positive. The negative thesis is that the “triviality results” do not support the rejection of Adams’s Thesis, because Lewisian “triviality based” arguments against Adams’s Thesis rest on an implausibly strong understanding of what it takes for some credal constraint to be a rational requirement (an understanding which Lewis himself later abandoned in other contexts). The positive thesis is that there is a simple (and plausible) way of modeling the probabilities of conditionals, which (a) obeys Adams’s Thesis, and (b) avoids all of the existing triviality results.

At-issueness in direct quotation: the case of Mayan quotatives

Scott AnderBois

In addition to verba dicendi, languages have a bunch of different other grammatical devices for encoding reported speech. While not common in Indo-European languages, two of the most common such elements cross-linguistically are reportative evidentials and quotatives. Quotatives have been much less discussed then either verba dicendi or reportatives, both in descriptive/typological literature and especially in formal semantic work. While quotatives haven’t been formally analyzed in detail previously to my knowledge, several recent works on reported speech constructions in general have suggested in passing that they pattern either with verba dicendi or with reportatives. Drawing on data from Yucatec Maya, I argue that they differ from both since they present direct quotation (like verba dicendi) but make a conventional at-issueness distinction (like reportatives). To account for these facts, I develop an account of quotatives by combining an extended Farkas & Bruce 2010-style discourse scoreboard with bicontextualism (building on Eckardt 2014’s work on Free Indirect Discourse).

An Introduction to Deep Fried Logic

Logic is Contractionless and Relevant, but Logic is (Accidentally) Contractionless and Relevant: An Introduction to Deep Fried Logic

Shay Logan

Logic, according to Beall, is the universal entailment relation. I claim that this forces us to accept that logic is contractionless and relevant. But neither relevance nor contraction-freedom, important as these features have been in the literature on logic and its philosophy, play a role in my argument. Instead, they are emergent features — logical accidents, if you will. Along the way I will familiarize us with a novel (and delicious) semantic theory that I call deep fried semantics.

How to compute with an infinite time Turing machine?

Sabrina Ouazzani

In this talk, we present infinite time Turing machines (ITTM), from the original definition of the model to some new infinite time algorithms.

We will present algorithmic techniques that allow to highlight some properties of the ITTM-computable ordinals. In particular, we will study gaps in ordinal computation times, that is to say, ordinal times at which no infinite time program halts.

Residuals and Conjugates in Positive Substructural Logics

Andrew Tedder

While the relations between an operation and its residuals play an essential role in substructural logic, a closely related relation between operations is that of conjugation — so closely related that with Boolean negation, the conjugates and residuals of an operation are interdefinable. In this talk extensions of Positive Non-Associative Lambek Calculus including conjugates (and residuals) of fusion are investigated. Some interesting properties of the conjugates are discussed, a proof system is presented, its adequacy questioned, and some further logics with conjugated operations are pondered.

Temporal reference in non-specific indefinites

Yael Sharvit

Non-specific indefinite noun phrases in attitude environments can be transparent or opaque. The interpretation of temporal expressions inside the indefinite is constrained by transparency/opacity. The first fact follows from standard assumptions about attitude reports; the second does not. I propose an account that derives both these facts.

Routley-Meyer relational semantics for some variants of Bradys´s 4-valued matrix

Sanda María López Velasco

On the one hand, the well-known logic BN4 was defined by R.T. Brady in 1982 and can be considered as the 4-valued logic of the relevant conditional. On the other hand, Routley-Meyer type ternary relational semantics is the semantics introduced by these authors in order to model the logic of relevance. Part of my current research involves applying a R-M semantics to different logics built upon some variants of MBN4 (the matrix of BN4) which verify the Routley and Meyer basic logic B.

The aim of this talk is to display these logics briefly and the reason why they could be of some interest. I will also explain how a R-M semantics can be applied to them.  Considering this, I will provide a general outline of the soundness and completeness theorems, valid for all these logics, and focus on the (corresponding) postulates proofs, which on the contrary need to be specified in each of these logics.